Digital Signature different everytime

Question

Digital signatures depend upon message and the secret key. Suppose receiver copies the message several times ( the reason for which we unique ids) , why will the signature be different (since the message and secret key are same)?

Answer 1

Bitcoin uses ECDSA, and the reason the signature is different for the same message and key is the random nonce, which is generated each time a signature is created.

An ECDSA signature is a pair (r,s) where r is the X coordinate of kG, and s = (m+r*x)/k (where k=nonce, m=message hash, x=private key, G=curve generator).

See also #3 in https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm#Signature_generation_algorithm